Trefoil knot in openscad with python https://youtu.be/aRY3jPGwudU?si=ywFVHaYWSELAbPo6

Here is the PythonSCAD variant. It does not need external Programs/Libraries https://www.thingiverse.com/thing:6065385/ from math import * fn=20 def knot(t): return [ sin(t)+2.0*sin(2.0*t), cos(t)-2.0*cos(2.0*t),sin(3.0*t)] n=150 pts=[] for i in range(n): pts.append(knot(2*3.1415926*i/n)) path_extrude(square(0.5),pts,twist=-120,closed=True).output() Greets from Austria On Sun, Oct 20, 2024 at 3:46 PM Sanjeev Prabhakar via Discuss < discuss@lists.openscad.org> wrote: > Trefoil knot in openscad with python > > https://youtu.be/aRY3jPGwudU?si=ywFVHaYWSELAbPo6 > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Not hard in pure OpenSCAD. This is an example from NopSCADlib's sweep test. knot = [ for(i=[0:.2:359]) [ (19*cos(3*i) + 40)*cos(2*i), (19*cos(3*i) + 40)*sin(2*i), 19*sin(3*i) ] ]; color("red") sweep(knot, circle_points(5), loop = true); [image: image.png] On Sun, 20 Oct 2024 at 15:28, Guenther Sohler via Discuss < discuss@lists.openscad.org> wrote: > Here is the PythonSCAD variant. It does not need external > Programs/Libraries > > https://www.thingiverse.com/thing:6065385/ > > from math import * > fn=20 > def knot(t): > return [ sin(t)+2.0*sin(2.0*t), cos(t)-2.0*cos(2.0*t),sin(3.0*t)] > n=150 > pts=[] > for i in range(n): > pts.append(knot(2*3.1415926*i/n)) > path_extrude(square(0.5),pts,twist=-120,closed=True).output() > > > Greets from Austria > > On Sun, Oct 20, 2024 at 3:46 PM Sanjeev Prabhakar via Discuss < > discuss@lists.openscad.org> wrote: > >> Trefoil knot in openscad with python >> >> https://youtu.be/aRY3jPGwudU?si=ywFVHaYWSELAbPo6 >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

On Sunday, October 20, 2024 at 10:28:44 AM EDT, Guenther Sohler via Discuss <discuss@lists.openscad.org> wrote: >Here is the PythonSCAD variant. It does not need external Programs/Libraries > >https://www.thingiverse.com/thing:6065385/ > >from math import * >fn=20 >def knot(t): >  return [ sin(t)+2.0*sin(2.0*t), cos(t)-2.0*cos(2.0*t),sin(3.0*t)] >n=150 >pts=[] >for i in range(n): >    pts.append(knot(2*3.1415926*i/n)) >path_extrude(square(0.5),pts,twist=-120,closed=True).output() When I tried that in the new OpenPythonSCAD I get: >ERROR: Traceback (most recent call last): >File "<string>", line 9, in <module> >NameError: name 'path_extrude' is not defined and had to add (of course) from openscad import * Once that was added, it worked as expected: William

Great You can try this to make a basket like structure: n=10 path=[ [10*(sin(d2r(t))+n*sin(n*d2r(t))), 10*(cos(d2r(t))-n*cos(n*d2r(t))), -30*cos((n+1)*d2r(t)) ] for t in range(0,360)] change the value of 'n' from 5 to 10 or more On Sun, 20 Oct 2024 at 20:43, William F. Adams via Discuss < discuss@lists.openscad.org> wrote: > On Sunday, October 20, 2024 at 10:28:44 AM EDT, Guenther Sohler via > Discuss <discuss@lists.openscad.org> wrote: > > >Here is the PythonSCAD variant. It does not need external > Programs/Libraries > > > >https://www.thingiverse.com/thing:6065385/ > > > >from math import * > >fn=20 > >def knot(t): > > return [ sin(t)+2.0*sin(2.0*t), cos(t)-2.0*cos(2.0*t),sin(3.0*t)] > >n=150 > >pts=[] > >for i in range(n): > > pts.append(knot(2*3.1415926*i/n)) > >path_extrude(square(0.5),pts,twist=-120,closed=True).output() > > When I tried that in the new OpenPythonSCAD I get: > > >ERROR: Traceback (most recent call last): > >File "<string>", line 9, in <module> > >NameError: name 'path_extrude' is not defined > > and had to add (of course) > > from openscad import * > > Once that was added, it worked as expected: > > > > William > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Here is a self-contained OpenSCAD only version: function flatten(vec) = [for (v=vec) for(e=v) e]; function rotQ(q, a, n) = Q_mult(flatten([cos(a/2),n*sin(a/2)]),q); function Q_mult(q,p) = [(q[0]*p[0]-q[1]*p[1]-q[2]*p[2]-q[3]*p[3]),(q[1]*p[0]+q[0]*p[1]+q[2]*p[3]-q[3]*p[2]),(q[2]*p[0]+q[0]*p[2]-q[1]*p[3]+q[3]*p[1]),(q[3]*p[0]+q[0]*p[3]+q[1]*p[2]-q[2]*p[1])]; function poly_addZ(list, z) = [for (v=list) [v[0], v[1], z]]; function poly_translate(list, d) = [for (v=list) v+d]; function poly_rotQ(list, q) = [for (v=list) Q_im(Q_mult(q,Q_mult([0,v.x,v.y,v.z],Q_conj(q))))]; function Q_im(q) = [q[1], q[2], q[3]]; function rot2d(x, a) = [cos(a)*x[0]+sin(a)*x[1], -sin(a)*x[0]+cos(a)*x[1]]; function poly_rot2d(list, a) = [for (v=list) rot2d(v, a)]; function Q_conj(q) = [q[0], -q[1], -q[2], -q[3]]; function poly_loft_faces (N_z, N_x, closed=false) = flatten([ (closed ? ([for (i=[0:N_x-1]) [(N_z-1)*N_x+i, (N_z-1)*N_x+(i+1)%N_x, i], for (i=[0:N_x-1]) [(i+1)%N_x, i, (N_z-1)*N_x+(i+1)%N_x]]) : concat([[for (i=[0:N_x-1]) N_x-1-i]], [[for (i=[0:N_x-1]) (N_z-1)*N_x+i]])), // caps for (i=[0:N_z-2],j=[0:N_x-1]) [[(i+1)*N_x+j, i*N_x+j, i*N_x+((j+1)%N_x)],[i*N_x+((j+1)%N_x), (i+1)*N_x+((j+1)%N_x), (i+1)*N_x+j]]]); module extrude (path, cr, closed=false, twist=0) { p = flatten([path, [2*path[len(path)-1]-path[len(path)-2]]]); pts = flatten([ for (i=1, d=p[1]-p[0], u=cross([0,0,1], d), un=norm(u), dn=norm(d), a=asin(un/dn), q=un>0?rotQ([1,0,0,0],a,u/un) : [1,0,0,0], n=d/dn, c=poly_addZ(cr,0); i<len(p); d=p[i]-path[i-1], u=cross(n, d), un=norm(u), dn=norm(d), a=asin(un/dn), n=d/dn,q=un>0?rotQ(q,a,u/un):q, i=i+1) poly_translate(poly_rotQ((twist!=0)?poly_addZ(poly_rot2d(cr,i*twist/(len(p)-1)),0):c, q), p[i-1]) ]); fcs = poly_loft_faces(len(path), len(cr), closed); polyhedron(pts, fcs, convexity=8); } myPath = [ for(t = [0:(360/360):359]) [ // trefoil knot 5*(.41*cos(t) - .18*sin(t) - .83*cos(2*t) - .83*sin(2*t) - .11*cos(3*t) + .27*sin(3*t)), 5*(.36*cos(t) + .27*sin(t) - 1.13*cos(2*t) + .30*sin(2*t) + .11*cos(3*t) - .27*sin(3*t)), 5*(.45*sin(t) - .30*cos(2*t) +1.13*sin(2*t) - .11*cos(3*t) + .27*sin(3*t))] ]; function rpoly_circle(r=1,pts=24) = [for (i=[0:pts-1]) r*[cos(i*360/pts), sin(-i*360/pts)]]; extrude(myPath, rpoly_circle(1.8, 60), closed=true, twist=-78); On Sun, Oct 20, 2024 at 11:57 AM Sanjeev Prabhakar via Discuss < discuss@lists.openscad.org> wrote: > Great > > You can try this to make a basket like structure: > > n=10 > path=[ [10*(sin(d2r(t))+n*sin(n*d2r(t))), > 10*(cos(d2r(t))-n*cos(n*d2r(t))), > -30*cos((n+1)*d2r(t)) > ] for t in range(0,360)] > > change the value of 'n' from 5 to 10 or more > > On Sun, 20 Oct 2024 at 20:43, William F. Adams via Discuss < > discuss@lists.openscad.org> wrote: > >> On Sunday, October 20, 2024 at 10:28:44 AM EDT, Guenther Sohler via >> Discuss <discuss@lists.openscad.org> wrote: >> >> >Here is the PythonSCAD variant. It does not need external >> Programs/Libraries >> > >> >https://www.thingiverse.com/thing:6065385/ >> > >> >from math import * >> >fn=20 >> >def knot(t): >> > return [ sin(t)+2.0*sin(2.0*t), cos(t)-2.0*cos(2.0*t),sin(3.0*t)] >> >n=150 >> >pts=[] >> >for i in range(n): >> > pts.append(knot(2*3.1415926*i/n)) >> >path_extrude(square(0.5),pts,twist=-120,closed=True).output() >> >> When I tried that in the new OpenPythonSCAD I get: >> >> >ERROR: Traceback (most recent call last): >> >File "<string>", line 9, in <module> >> >NameError: name 'path_extrude' is not defined >> >> and had to add (of course) >> >> from openscad import * >> >> Once that was added, it worked as expected: >> >> >> >> William >> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Easy geometric explanation on cinquefoil torus knots https://youtu.be/tRWPeoyQhWs?si=Nx63gUabK-AUWELE On Sun, 20 Oct, 2024, 7:15 pm Sanjeev Prabhakar, <sprabhakar2006@gmail.com> wrote: > Trefoil knot in openscad with python > > https://youtu.be/aRY3jPGwudU?si=ywFVHaYWSELAbPo6 >